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The dual-tree complex wavelet transform (DTCWT) is an enhancement of theconventional discrete wavelet transform (DWT) due to a higher degree ofshift-invariance and a greater directional selectivity, finding itsapplications in signal and image processing. This paper presents a quantitativeproof of the superiority of the DTCWT over the DWT in case of modulatedwavelets.

The near shift-invariance of the dual-tree complex wavelet transform revisited